We present a multi-wavelength analysis of galaxies selected at 450 and 850um from the deepest SCUBA-2 observations in the Extended Groth Strip (EGS) field, which have an average depth of sigma_450=1.9 and sigma_850=0.46 mJy/beam over ~70 sq. arcmin. The final sample comprises 95 sources: 56 (59%) are detected at both wavelengths, 31 (33%) are detected only at 850um, and 8 (8%) are detected only at 450um. We identify counterparts for 75% of the whole sample. The redshift distributions of the 450 and 850um samples peak at different redshifts with median values of z=1.66 +/- 0.18 and z=2.30 +/- 0.20, respectively. However, the two populations have similar IR luminosities, SFRs, and stellar masses, with mean values of (1.5 +/- 0.2) x 10^12 L_sun, (150 +/- 20) M_sun/yr, and (9.0 +/- 0.6) x 10^10 M_sun, respectively. This places most of our sources (>85%) on the high-mass end of the `main-sequence of star-forming galaxies. Exploring the IR excess vs UV-slope (IRX-beta) relation we find that the most luminous galaxies are consistent with the Meurer law, while the less luminous galaxies lie below this relation. Using the results of a two-dimensional modelling of the HST H_160-band imaging, we derive a median Sersic index of n=1.4 +0.3 -0.1 and a median half-light radius of R_1/2 = 4.8 +/ 0.4 kpc. Based on a visual-like classification in the same band, we find that the dominant component for most of the galaxies at all redshifts is a disk-like structure, although there is a transition from irregular disks to disks with a spheroidal component at z~1.4, which morphologically supports the scenario of SMGs as progenitors of massive elliptical galaxies.